Pomerance, Carl
Overview
Works:  32 works in 162 publications in 3 languages and 3,744 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Editor, Author, Other 
Publication Timeline
.
Most widely held works by
Carl Pomerance
Prime numbers : a computational perspective by
Richard E Crandall(
Book
)
41 editions published between 2001 and 2010 in English and Undetermined and held by 1,599 WorldCat member libraries worldwide
Prime numbers beckon to the beginner, as the basic notion of primality is accessible even to children. Yet, some of the simplest questions about primes have confounded humankind for millennia. In the new edition of this highly successful book, Richard Crandall and Carl Pomerance have provided updated material on theoretical, computational, and algorithmic fronts. New results discussed include the AKS test for recognizing primes, computational evidence for the Riemann hypothesis, a fast binary algorithm for the greatest common divisor, nonuniform fast Fourier transforms, and more. The authors also list new computational records and survey new developments in the theory of prime numbers, including the magnificent proof that there are arbitrarily long arithmetic progressions of primes, and the final resolution of the Catalan problem. Numerous exercises have been added. Richard Crandall currently holds the title of Apple Distinguished Scientist, having previously been Apple's Chief Cryptographer, the Chief Scientist at NeXT, Inc., and recipient of the Vollum Chair of Science at Reed College. Though he publishes in quantum physics, biology, mathematics, and chemistry, and holds various engineering patents, his primary interest is interdisciplinary scientific computation. Carl Pomerance is the recipient of the Chauvenet and Conant Prizes for expository mathematical writing. He is currently a mathematics professor at Dartmouth College, having previously been at the University of Georgia and Bell Labs. A popular lecturer, he is well known for his research in computational number theory, his efforts having produced important algorithms now in use. From the reviews of the first edition: "Destined to become a definitive textbook conveying the most modern computational ideas about prime numbers and factoring, this book will stand as an excellent reference for this kind of computation, and thus be of interest to both educators and researchers." ^ L'Enseignement Mathématique "...Prime Numbers is a welcome addition to the literature of number theorycomprehensive, uptodate and written with style."  American Scientist "It's rare to say this of a math book, but open Prime Numbers to a random page and it's hard to put down. Crandall and Pomerance have written a terrific book."  Bulletin of the AMS
41 editions published between 2001 and 2010 in English and Undetermined and held by 1,599 WorldCat member libraries worldwide
Prime numbers beckon to the beginner, as the basic notion of primality is accessible even to children. Yet, some of the simplest questions about primes have confounded humankind for millennia. In the new edition of this highly successful book, Richard Crandall and Carl Pomerance have provided updated material on theoretical, computational, and algorithmic fronts. New results discussed include the AKS test for recognizing primes, computational evidence for the Riemann hypothesis, a fast binary algorithm for the greatest common divisor, nonuniform fast Fourier transforms, and more. The authors also list new computational records and survey new developments in the theory of prime numbers, including the magnificent proof that there are arbitrarily long arithmetic progressions of primes, and the final resolution of the Catalan problem. Numerous exercises have been added. Richard Crandall currently holds the title of Apple Distinguished Scientist, having previously been Apple's Chief Cryptographer, the Chief Scientist at NeXT, Inc., and recipient of the Vollum Chair of Science at Reed College. Though he publishes in quantum physics, biology, mathematics, and chemistry, and holds various engineering patents, his primary interest is interdisciplinary scientific computation. Carl Pomerance is the recipient of the Chauvenet and Conant Prizes for expository mathematical writing. He is currently a mathematics professor at Dartmouth College, having previously been at the University of Georgia and Bell Labs. A popular lecturer, he is well known for his research in computational number theory, his efforts having produced important algorithms now in use. From the reviews of the first edition: "Destined to become a definitive textbook conveying the most modern computational ideas about prime numbers and factoring, this book will stand as an excellent reference for this kind of computation, and thus be of interest to both educators and researchers." ^ L'Enseignement Mathématique "...Prime Numbers is a welcome addition to the literature of number theorycomprehensive, uptodate and written with style."  American Scientist "It's rare to say this of a math book, but open Prime Numbers to a random page and it's hard to put down. Crandall and Pomerance have written a terrific book."  Bulletin of the AMS
Cryptology and computational number theory by
Carl Pomerance(
Book
)
19 editions published between 1990 and 2014 in English and held by 439 WorldCat member libraries worldwide
19 editions published between 1990 and 2014 in English and held by 439 WorldCat member libraries worldwide
Advances in cryptologyCRYPTO '87 : proceedings by
Carl Pomerance(
Book
)
22 editions published between 1987 and 2007 in English and Undetermined and held by 390 WorldCat member libraries worldwide
This book is the proceedings of CRYPTO '87, one in a series of annual conferences devoted to cryptologic research. CRYPTO '87 was attended by 170 people representing 19 countries. The papers in this volume are presented in seven sections. The first six sections comprise all of the papers on the regular program, including two papers that were not presented at the meeting. The seventh section contains some of the papers presented at a "Rump Session". The main sections deal with the following topics: communication networks and standards; protocols; key distribution systems; public key systems; design and analysis of cryptographic systems; and applications
22 editions published between 1987 and 2007 in English and Undetermined and held by 390 WorldCat member libraries worldwide
This book is the proceedings of CRYPTO '87, one in a series of annual conferences devoted to cryptologic research. CRYPTO '87 was attended by 170 people representing 19 countries. The papers in this volume are presented in seven sections. The first six sections comprise all of the papers on the regular program, including two papers that were not presented at the meeting. The seventh section contains some of the papers presented at a "Rump Session". The main sections deal with the following topics: communication networks and standards; protocols; key distribution systems; public key systems; design and analysis of cryptographic systems; and applications
Combinatorial Number Theory by
Bruce M Landman(
)
1 edition published in 2009 in English and held by 360 WorldCat member libraries worldwide
This volume contains refereed papers related to the lectures given at a conference in number theory, the?Integers Conference 2007?, which was held at the University of West Georgia in October 2007, with many distinguished speakers including Neil Hindman, Melvyn Nathanson, Richard Nowakowski, Carl Pomerance, and many others
1 edition published in 2009 in English and held by 360 WorldCat member libraries worldwide
This volume contains refereed papers related to the lectures given at a conference in number theory, the?Integers Conference 2007?, which was held at the University of West Georgia in October 2007, with many distinguished speakers including Neil Hindman, Melvyn Nathanson, Richard Nowakowski, Carl Pomerance, and many others
Advances in cryptology : Conference on the theory and applications of cryptographic techniques : Papers by CRYPTO (Conference)(
)
7 editions published in 1988 in English and held by 265 WorldCat member libraries worldwide
This book is the proceedings of CRYPTO '87, one in a series of annual conferences devoted to cryptologic research. CRYPTO '87 was attended by 170 people representing 19 countries. The papers in this volume are presented in seven sections. The first six sections comprise all of the papers on the regular program, including two papers that were not presented at the meeting. The seventh section contains some of the papers presented at a "Rump Session". The main sections deal with the following topics: communication networks and standards; protocols; key distribution systems; public key systems; design and analysis of cryptographic systems; and applications
7 editions published in 1988 in English and held by 265 WorldCat member libraries worldwide
This book is the proceedings of CRYPTO '87, one in a series of annual conferences devoted to cryptologic research. CRYPTO '87 was attended by 170 people representing 19 countries. The papers in this volume are presented in seven sections. The first six sections comprise all of the papers on the regular program, including two papers that were not presented at the meeting. The seventh section contains some of the papers presented at a "Rump Session". The main sections deal with the following topics: communication networks and standards; protocols; key distribution systems; public key systems; design and analysis of cryptographic systems; and applications
Analytic number theory : in honor of Helmut Maier's 60th birthday(
)
12 editions published in 2015 in English and held by 264 WorldCat member libraries worldwide
This volume contains a collection of research and survey papers written by some of the most eminent mathematicians in the international community and is dedicated to Helmut Maier, whose own research has been groundbreaking and deeply influential to the field. Specific emphasis is given to topics regarding exponential and trigonometric sums and their behavior in short intervals, anatomy of integers and cyclotomic polynomials, small gaps in sequences of sifted prime numbers, oscillation theorems for primes in arithmetic progressions, inequalities related to the distribution of primes in short intervals, the Möbius function, Euler's totient function, the Riemann zeta function and the Riemann Hypothesis. Graduate students, research mathematicians, as well as computer scientists and engineers who are interested in pure and interdisciplinary research, will find this volume a useful resource. Contributors to this volume: Bill Allombert, Levent Alpoge, Nadine Amersi, Yuri Bilu, Régis de la Bretèche, Christian Elsholtz, John B. Friedlander, Kevin Ford, Daniel A. Goldston, Steven M. Gonek, Andrew Granville, Adam J. Harper, Glyn Harman, D.R. HeathBrown, Aleksandar Ivić, Geoffrey Iyer, Jerzy Kaczorowski, Daniel M. Kane, Sergei Konyagin, Dimitris Koukoulopoulos, Michel L. Lapidus, Oleg Lazarev, Andrew H. Ledoan, Robert J. Lemke Oliver, Florian Luca, James Maynard, Steven J. Miller, Hugh L. Montgomery, Melvyn B. Nathanson, Ashkan Nikeghbali, Alberto Perelli, Amalia PizarroMadariaga, János Pintz, Paul Pollack, Carl Pomerance, Michael Th. Rassias, Maksym Radziwiłł, Joël Rivat, András Sárközy, Jeffrey Shallit, Terence Tao, Gérald Tenenbaum, László Tóth, Tamar Ziegler, Liyang Zhang
12 editions published in 2015 in English and held by 264 WorldCat member libraries worldwide
This volume contains a collection of research and survey papers written by some of the most eminent mathematicians in the international community and is dedicated to Helmut Maier, whose own research has been groundbreaking and deeply influential to the field. Specific emphasis is given to topics regarding exponential and trigonometric sums and their behavior in short intervals, anatomy of integers and cyclotomic polynomials, small gaps in sequences of sifted prime numbers, oscillation theorems for primes in arithmetic progressions, inequalities related to the distribution of primes in short intervals, the Möbius function, Euler's totient function, the Riemann zeta function and the Riemann Hypothesis. Graduate students, research mathematicians, as well as computer scientists and engineers who are interested in pure and interdisciplinary research, will find this volume a useful resource. Contributors to this volume: Bill Allombert, Levent Alpoge, Nadine Amersi, Yuri Bilu, Régis de la Bretèche, Christian Elsholtz, John B. Friedlander, Kevin Ford, Daniel A. Goldston, Steven M. Gonek, Andrew Granville, Adam J. Harper, Glyn Harman, D.R. HeathBrown, Aleksandar Ivić, Geoffrey Iyer, Jerzy Kaczorowski, Daniel M. Kane, Sergei Konyagin, Dimitris Koukoulopoulos, Michel L. Lapidus, Oleg Lazarev, Andrew H. Ledoan, Robert J. Lemke Oliver, Florian Luca, James Maynard, Steven J. Miller, Hugh L. Montgomery, Melvyn B. Nathanson, Ashkan Nikeghbali, Alberto Perelli, Amalia PizarroMadariaga, János Pintz, Paul Pollack, Carl Pomerance, Michael Th. Rassias, Maksym Radziwiłł, Joël Rivat, András Sárközy, Jeffrey Shallit, Terence Tao, Gérald Tenenbaum, László Tóth, Tamar Ziegler, Liyang Zhang
Lecture notes on primality testing and factoring : a short course at Kent State University by
Carl Pomerance(
Book
)
10 editions published between 1934 and 1984 in English and held by 226 WorldCat member libraries worldwide
10 editions published between 1934 and 1984 in English and held by 226 WorldCat member libraries worldwide
Combinatorial number theory : proceedings of the "Integers Conference 2005" in celebration of the 70th birthday of Ronald
Graham, Carrollton, Georgia, USA, October 2730, 2005 by
Jaroslav Nesetril(
)
11 editions published between 2007 and 2013 in English and held by 61 WorldCat member libraries worldwide
This carefully edited volume contains selected refereed papers based on lectures presented by many distinguished speakers at the "Integers Conference 2005", an international conference in combinatorial number theory. The conference was held in celebration of the 70th birthday of Ronald Graham, a leader in several fields of mathematics
11 editions published between 2007 and 2013 in English and held by 61 WorldCat member libraries worldwide
This carefully edited volume contains selected refereed papers based on lectures presented by many distinguished speakers at the "Integers Conference 2005", an international conference in combinatorial number theory. The conference was held in celebration of the 70th birthday of Ronald Graham, a leader in several fields of mathematics
Advances in Cryptology  CRYPTO '87 : Proceedings by
Carl Pomerance(
)
3 editions published between 1986 and 2006 in English and Undetermined and held by 42 WorldCat member libraries worldwide
3 editions published between 1986 and 2006 in English and Undetermined and held by 42 WorldCat member libraries worldwide
Cryptology and computational number theory : [lecture notes prepared for the American Mathematical Society Short Course Cryptology
and Computational Number Theory, held in Boulder, Colorado, August 67, 1989](
Book
)
1 edition published in 1990 in English and held by 22 WorldCat member libraries worldwide
1 edition published in 1990 in English and held by 22 WorldCat member libraries worldwide
Advances in Cryptology  CRYPTO 87 by
Carl Pomerance(
)
3 editions published in 1988 in English and held by 15 WorldCat member libraries worldwide
Zeroknowledge interactive proofsystems are a new technique which can be used as a cryptographic tool for designing provably secure protocols. Goldwasser, Micali, and Rackoff originally suggested this technique for controlling the knowledge released in an interactive proof of membership in a language, and for classification of languages [19]. In this approach, knowledge is defined in terms of complexity to convey knowledge if it gives a computational advantage to the receiver, theory, and a message is said for example by giving him the result of an intractable computation. The formal model of interacting machines is described in [19, 15, 171. A proofsystem (for a language L) is an interactive protocol by which one user, the prover, attempts to convince another user, the verifier, that a given input x is in L. We assume that the verifier is a probabilistic machine which is limited to expected polynomialtime computation, while the prover is an unlimited probabilistic machine. (In cryptographic applications the prover has some trapdoor information, or knows the cleartext of a publicly known ciphertext) A correct proofsystem must have the following properties: If XE L, the prover will convince the verifier to accept the pmf with very high probability. If XP L no prover, no matter what program it follows, is able to convince the verifier to accept the proof, except with vanishingly small probability
3 editions published in 1988 in English and held by 15 WorldCat member libraries worldwide
Zeroknowledge interactive proofsystems are a new technique which can be used as a cryptographic tool for designing provably secure protocols. Goldwasser, Micali, and Rackoff originally suggested this technique for controlling the knowledge released in an interactive proof of membership in a language, and for classification of languages [19]. In this approach, knowledge is defined in terms of complexity to convey knowledge if it gives a computational advantage to the receiver, theory, and a message is said for example by giving him the result of an intractable computation. The formal model of interacting machines is described in [19, 15, 171. A proofsystem (for a language L) is an interactive protocol by which one user, the prover, attempts to convince another user, the verifier, that a given input x is in L. We assume that the verifier is a probabilistic machine which is limited to expected polynomialtime computation, while the prover is an unlimited probabilistic machine. (In cryptographic applications the prover has some trapdoor information, or knows the cleartext of a publicly known ciphertext) A correct proofsystem must have the following properties: If XE L, the prover will convince the verifier to accept the pmf with very high probability. If XP L no prover, no matter what program it follows, is able to convince the verifier to accept the proof, except with vanishingly small probability
Prime Numbers a Computational Perspective by
Richard E Crandall(
)
2 editions published in 2005 in Undetermined and English and held by 11 WorldCat member libraries worldwide
Prime numbers beckon to the beginner, as the basic notion of primality is accessible even to children. Yet, some of the simplest questions about primes have confounded humankind for millennia. In the new edition of this highly successful book, Richard Crandall and Carl Pomerance have provided updated material on theoretical, computational, and algorithmic fronts. New results discussed include the AKS test for recognizing primes, computational evidence for the Riemann hypothesis, a fast binary algorithm for the greatest common divisor, nonuniform fast Fourier transforms, and more. The authors also list new computational records and survey new developments in the theory of prime numbers, including the magnificent proof that there are arbitrarily long arithmetic progressions of primes, and the final resolution of the Catalan problem. Numerous exercises have been added. Richard Crandall currently holds the title of Apple Distinguished Scientist, having previously been Apple's Chief Cryptographer, the Chief Scientist at NeXT, Inc., and recipient of the Vollum Chair of Science at Reed College. Though he publishes in quantum physics, biology, mathematics, and chemistry, and holds various engineering patents, his primary interest is interdisciplinary scientific computation. Carl Pomerance is the recipient of the Chauvenet and Conant Prizes for expository mathematical writing. He is currently a mathematics professor at Dartmouth College, having previously been at the University of Georgia and Bell Labs. A popular lecturer, he is well known for his research in computational number theory, his efforts having produced important algorithms now in use. From the reviews of the first edition: "Destined to become a definitive textbook conveying the most modern computational ideas about prime numbers and factoring, this book will stand as an excellent reference for this kind of computation, and thus be of interest to both educators and researchers." < L'Enseignement Mathématique " ... Prime Numbers is a welcome addition to the literature of number theorycomprehensive, uptodate and written with style."American Scientist "It's rare to say this of a math book, but open Prime Numbers to a random page and it's hard to put down. Crandall and Pomerance have written a terrific book."  Bulletin of the AMS
2 editions published in 2005 in Undetermined and English and held by 11 WorldCat member libraries worldwide
Prime numbers beckon to the beginner, as the basic notion of primality is accessible even to children. Yet, some of the simplest questions about primes have confounded humankind for millennia. In the new edition of this highly successful book, Richard Crandall and Carl Pomerance have provided updated material on theoretical, computational, and algorithmic fronts. New results discussed include the AKS test for recognizing primes, computational evidence for the Riemann hypothesis, a fast binary algorithm for the greatest common divisor, nonuniform fast Fourier transforms, and more. The authors also list new computational records and survey new developments in the theory of prime numbers, including the magnificent proof that there are arbitrarily long arithmetic progressions of primes, and the final resolution of the Catalan problem. Numerous exercises have been added. Richard Crandall currently holds the title of Apple Distinguished Scientist, having previously been Apple's Chief Cryptographer, the Chief Scientist at NeXT, Inc., and recipient of the Vollum Chair of Science at Reed College. Though he publishes in quantum physics, biology, mathematics, and chemistry, and holds various engineering patents, his primary interest is interdisciplinary scientific computation. Carl Pomerance is the recipient of the Chauvenet and Conant Prizes for expository mathematical writing. He is currently a mathematics professor at Dartmouth College, having previously been at the University of Georgia and Bell Labs. A popular lecturer, he is well known for his research in computational number theory, his efforts having produced important algorithms now in use. From the reviews of the first edition: "Destined to become a definitive textbook conveying the most modern computational ideas about prime numbers and factoring, this book will stand as an excellent reference for this kind of computation, and thus be of interest to both educators and researchers." < L'Enseignement Mathématique " ... Prime Numbers is a welcome addition to the literature of number theorycomprehensive, uptodate and written with style."American Scientist "It's rare to say this of a math book, but open Prime Numbers to a random page and it's hard to put down. Crandall and Pomerance have written a terrific book."  Bulletin of the AMS
Cryptology and computational number theory(
Book
)
1 edition published in 1990 in English and held by 9 WorldCat member libraries worldwide
1 edition published in 1990 in English and held by 9 WorldCat member libraries worldwide
Advances in cryptology : proceedings : CRYPTO '87 by University of California(
Book
)
2 editions published in 1988 in English and held by 9 WorldCat member libraries worldwide
2 editions published in 1988 in English and held by 9 WorldCat member libraries worldwide
Advances in cryptology  CRYPTO '87 : proceedings by
Carl Pomerance(
Book
)
4 editions published in 1988 in English and Italian and held by 7 WorldCat member libraries worldwide
4 editions published in 1988 in English and Italian and held by 7 WorldCat member libraries worldwide
Average case error estimates for the strong probable prime test by
I. B Damgård(
Book
)
3 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
Advances in cryptology, CRIPTO'87 : Proceedings of a Conference on the Theory and Applications of Cryptographic Techniques,
held at the University of California, Santa Barbara, August 1620,1987(
Book
)
3 editions published between 1988 and 2006 in English and held by 4 WorldCat member libraries worldwide
3 editions published between 1988 and 2006 in English and held by 4 WorldCat member libraries worldwide
Sosu zensho : Keisan karano apurochi by
Richard E Crandall(
Book
)
2 editions published in 2010 in Japanese and held by 3 WorldCat member libraries worldwide
2 editions published in 2010 in Japanese and held by 3 WorldCat member libraries worldwide
The smallest nuniform hypergraph with positive discrepancy by
Inc Bell Communications Research(
Book
)
2 editions published in 1986 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1986 in English and held by 2 WorldCat member libraries worldwide
A pipeline architecture for factoring large integers with the quadratic sieve algorithm by
Carl Pomerance(
Book
)
1 edition published in 1986 in English and held by 1 WorldCat member library worldwide
1 edition published in 1986 in English and held by 1 WorldCat member library worldwide
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Related Identities
 Crandall, Richard E. 19472012 Author
 Goldwasser, S. (Shafi) 1958 Other
 Landman, Bruce Author Editor
 Nathanson, Melvyn B. Editor
 Robertson, Aaron Editor
 Nesetril, Jaroslav
 International Association for Cryptologic Research
 IEEE Computer Society Technical Committee on Security and Privacy
 University of California, Santa Barbara Computer Science Department
 Rassias, Michael Th 1987 Editor
Useful Links
Associated Subjects
Combinatorial number theory ComputersAccess control Computer science Computer security Cryptography Data encryption (Computer science) Data structures (Computer science) Data transmission systemsSecurity measures Mathematical analysis Mathematics Numbers, Natural Numbers, Prime Number theory Numerical analysis
Covers
Alternative Names
Carl Pomerance American mathematician
Carl Pomerance Amerikaans wiskundige
Carl Pomerance amerikansk matematikar
Carl Pomerance amerikansk matematiker
Carl Pomerance matemático estadounidense
Carl Pomerance matematico statunitense
Carl Pomerance mathématicien américain
Carl Pomerance USamerikanischer Zahlentheoretiker
Pomerance, C.
Pomerance, Carl B.
Карл Померанс
קארל פומרנץ
קארל פומרנץ מתמטיקאי אמריקאי
カール・ポメランス
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